Thanks, I see. But how does one decide whether someone believes something about the comment, or is just punishing generally? I guess we might require a comment if there is a down vote? Or the moderators could look at voting patterns overall, or in special cases where attention has been called. I am new to LW so I have little sense of context.
Oops. Thanks for the fix!
Source? Or just your n = 1 observation?
No offense taken. I am sorry I did not get to see Gill & Robins at JSM. Jamie also talks about some of these issues online back in 2013 at https://www.youtube.com/watch?v=rjcoJ0gC_po
I think people should vote how they believe, up or down. But I feel very strongly that we should each have 1 vote.
Rather than define it, here is a (purported, I don't recall this one from Beyond Good and Evil) quote:
When a woman has scholarly inclinations there is usually something wrong with her sexuality. – Friedrich Nietzsche
I will assume by likelihood you meant probability. I think you have removed by concern by conditioning on it. The theorem has probability 1, in your formal system. For me that is not probability 1, I don't give any formal system full control of my beliefs/probabilities.
Of course, I believe arithmetic with probability approaching 1. For now.
I think one of the clearest expositions on these issues is ET Jaynes. The first three chapters (which is some of the relevant part) can be found at http://bayes.wustl.edu/etj/prob/book.pdf.
Have you read Nietzsche? I read Beyond Good and Evil. He seemed like a misogynist asshole, but perhaps just a product if his time.
Great question. I believe Jack Good's answer was his "type 2 rationality", which implies a Bayes/non-Bayes synthesis, semiparametric statistics, and nondogmatism.
Exciting! If I were in your place I would look at the growing field of causal inference which lives at the interface of statistics, computer science, epidemiology and economics. The books by Hernan and Robins (causal inference) and Pearl (causality), as well as the journal edited by Judea Pearl and Maya Petersen (causal inference).
Beyond all doubt sounds fairly dogmatic, no? Godel proved in 1931 that Hilbert's program for a solid mathematical foundation (circa 1900) was impossible.
I get your point that we can have greater belief in logical and mathematical knowledge. But (as pointed out by JoshuaZ) I have seen too many errors in proofs given at scientific meetings (and in submitted publications) to blindly believe just about anything.
Sounds like this is perhaps related to the counterfactual-consistency statement? In its simple form, that the counterfactual or potential outcome under policy "a" equals the factual observed outcome when you in fact undertake policy "a", or formally, Y^a = Y when A = a.
Pearl has a nice (easy) discussion in the journal Epidemiology (http://www.ncbi.nlm.nih.gov/pubmed/20864888).
Is this what you are getting at, or am I missing the point?
Ilya, can you give me a definition of "counterfactual definiteness" please?
Has there been discussion of Jack Good's principle of nondogmatism? (see Good Thinking, page 30).
The principle, stated simply in my bastardized version, is to believe no thing with probability 1. It seems to underlie Good's type 2 rationality (to maximize expected utility, within reason).
This is (almost) in accord with Lindley's concept of Cromwell's rule (see Lindley's Understanding Uncertainty or https://en.wikipedia.org/wiki/Cromwell%27s_rule). And seems to be closely related to Jaynes' mind projection fallacy.
"Irrationality is intellectual violence against which the pacifism of rationality may or may not be an adequate weapon."
This is not evidence, this is opinion. Granted, good evidence on these points is hard to come by. But treating opinion like fact is detrimental to communication.
Seems my opinions differ from yours. We have different utility functions with respect to these issues. You get yours, I get mine. On any joint decision for a shared utility we each get weight 1/n.
I pose we should spend our time/resources not arguing about our utilities, but collecting high-quality evidence to improve the probability portions of our MEU.